Game of Strategy Having Dividable Game Pieces

ABSTRACT

A game of strategy includes a plurality of game pieces that are dividable into smaller game pieces. The game pieces initially comprise some in a first color and some in a second color. The game pieces are arranged in a pattern on a playing surface to define a playing field. Each of the pieces has a legal shape such that the pieces may only be divided into legal shapes. The game pieces may be one or more of divided, joined, swapped and captured during play. A process for playing a game of strategy is also described. A winning position for a game of strategy includes a contiguous chain of game pieces of a single color that extends from one or both of the left side to the right side and the top side to the bottom side of a playing field. A notation system for describing the moves of play is also described.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims priority to U.S. Provisional Application No.61/117,948 filed on Nov. 25, 2008, the disclosure of which isincorporated herein by reference in its entirety.

FIELD OF THE INVENTION

This technology relates to a game of strategy that includes game piecesthat are dividable into smaller pieces, joinable into larger pieces, andreplaceable among one another from a starting position, to a pluralityof intermediate positions, to a winning position.

BACKGROUND

Known games of strategy include chess and checkers. Each has their ownrules with many exceptions to the rules.

SUMMARY

A strategy game is shown and described.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 depicts an example of neighboring pieces of the game;

FIG. 2 depicts another example of neighboring pieces of the game;

FIG. 3 depicts an example of pieces that are not neighboring;

FIG. 4 depicts another example of pieces that are not neighboring;

FIG. 5 depicts an example of legal size pieces and non-legal size piecesof the game;

FIG. 6 depicts the starting position of the pieces of the game;

FIG. 7 a depicts an example of splitting a game piece during play;

FIG. 7 b depicts another example of splitting a game piece during play;

FIG. 8 a depicts an example of splitting of multiple game pieces duringplay;

FIG. 8 b depicts another example of splitting of multiple game piecesduring play;

FIG. 9 a depicts an examples of joining of game pieces during play;

FIG. 9 b depicts another example of joining of game pieces during play;

FIG. 9 c depicts yet another example of joining of game pieces duringplay;

FIG. 9 d depicts a further example of joining of game pieces duringplay;

FIG. 10 depicts examples of pieces that may swap with one anotherbecause of the borders they share;

FIG. 11 depicts examples of pieces that may not swap with one anotherbecause they are not two-point neighbors;

FIG. 12 depicts an example move of the black player that involvessplitting and swapping in progression;

FIG. 13 depicts another example move of the black player that involvessplitting and swapping in progression;

FIG. 14 depicts the pieces of the game after the black player haspositioned his or her pieces to capture a single white player's piece;

FIG. 15 depicts the pieces of the game after the black player haspositioned his or her pieces to capture multiple white player's pieces;

FIG. 16 depicts the pieces of the game after the black player haspositioned his or her pieces to capture multiple white players' pieces;

FIG. 17 a depicts a starting position of an example move of the blackplayer that involves splitting, swapping, and capturing in progression;

FIG. 17 b depicts a move from the starting position shown in FIG. 17 a;

FIG. 17 c depicts a move from the position shown in FIG. 17 b;

FIG. 17 d depicts a move from the position shown in FIG. 17 c;

FIG. 17 e depicts a move from the position shown in FIG. 17 d;

FIG. 17 f depicts a move from the position shown in FIG. 17 e;

FIG. 17 g depicts a move from the position shown in FIG. 17 f;

FIG. 17 h depicts a move from the position shown in FIG. 17 g;

FIG. 17 i depicts a move from the position shown in FIG. 17 h;

FIG. 18 depicts the pieces of the game after a first turn has been takenby the black player;

FIG. 19 depicts the pieces of the game after many turns have been takenby both black and white players, but not in a winning position;

FIG. 20 depicts an example position where the black player is about tomove and win the game;

FIG. 21 depicts the black player's winning move from FIG. 20;

FIG. 22 depicts the pieces of the game after an alternative first turnhas been taken by the black player;

FIG. 23 depicts the pieces of the game in the middle of play, withneither the black player nor the white player about to move into awinning position;

FIG. 24 depicts the pieces of the game at a later time than is shown inFIG. 23, with the White player about to move to win the game;

FIG. 25 depicts the pieces of the game after the White player has made amove from FIG. 24 to win the game, showing the winning position;

FIG. 26 depicts an example location used in notating a move in theexample game;

FIG. 27 depicts another example location used in notating a move in theexample game;

FIG. 28 depicts another example location used in notating a move in theexample game;

FIG. 29 depicts yet another example location used in notating a move inthe example game;

FIG. 30 depicts another example location used in notating a move in theexample game;

FIG. 31 depicts a further example location used in notating a move inthe example game;

FIG. 32 a depicts a starting position for a join;

FIG. 32 b depicts an ending position in the same playing field as FIG.32 a after pieces have been joined;

FIG. 33 a depicts the playing field before pieces are joined;

FIG. 33 b depicts the same playing field as FIG. 33 a after pieces havebeen joined and then swapped to the West;

FIG. 34 a depicts the playing field before pieces are split on avertical split-line;

FIG. 34 b depicts the same playing field as FIG. 34 a after the pieceshave been split on a vertical split-line and swapped to the East;

FIG. 35 a depicts the playing field before pieces are split on ahorizontal split-line;

FIG. 35 b depicts the playing field of FIG. 35 a after pieces have beensplit on a horizontal split-line and swapped to the East;

FIG. 36 a depicts the playing field before pieces are split along ahorizontal split-line;

FIG. 36 b depicts the playing field of FIG. 36 a after pieces have beensplit and the northern most split piece is swapped to the West;

FIG. 37 a depicts the playing field before multiple pieces that arepositioned adjacent one another are split horizontally;

FIG. 37 b depicts the playing field of FIG. 37 a after multiple pieceshave been split;

FIG. 38 a depicts the playing field before multiple pieces that are notpositioned adjacent one another are split vertically;

FIG. 38 b depicts the playing field of FIG. 38 a after multiple piecesare split vertically;

FIG. 39 depicts the playing field of FIG. 38 b after multiple pieceshave been split vertically and illustrates a series of swaps that areperformed on the lower, East split piece, with swaps occurring in theEast, North, and East directions;

FIG. 40 depicts the playing field of FIG. 38 b after multiple pieceshave been split vertically and illustrates a series of swaps that areperformed on the lower, West piece, with swaps occurring in the North,West, and North directions;

FIG. 41 depicts the playing field of FIG. 38 b after multiple pieceshave been split vertically and illustrates a series of swaps that areperformed on the upper, East piece, with swaps occurring in the East,South, and East directions;

FIG. 42 depicts the playing field of FIG. 38 b after multiple pieceshave been split vertically and illustrates a series of swaps that areperformed on the upper, West piece, with swaps occurring in the West,South, South, and East directions;

FIG. 43 depicts a golden rectangle;

FIG. 44 depicts a silver rectangle; and

FIG. 45 depicts an A4 rectangle and the various ways that an A4rectangle can be split.

DETAILED DESCRIPTION

The example game is a turn-based strategy game for two players thatincludes a plurality of pieces. The pieces, in the examples depicted,include a plurality of tile-like pieces that are rectangular. The piecesare two different colors, such as black and white. A first playercontrols the black pieces 10 and a second player controls the whitepieces 12. Each player tries to connect their pieces into chains ofneighboring pieces. The tile-like pieces may be laid out on a gameboard, on a table top, or on any flat surface in order to define aplaying field. The playing field may be rectangular, including square.There may be instances where one of skill in the art may define theplaying field in a non-rectangular manner. A game board is notabsolutely necessary, but may be used if desired. A game board may bedesigned and provided that helps to maintain the pieces in the shapesshown in the figures.

The pieces are positioned adjacent one another and can be “squared”against one another periodically, as desired, during play. The piecesmay be squared against one another by closing any gaps between thepieces by pushing them together, such as by pressing the outer edges ofthe playing field together. A tool can be designed to assist withsquaring. Such a tool may be a straight edge of sturdy material or aruler-like apparatus.

The example game includes legal shaped pieces, which are either squareor rectangular. For ease of description, a square is defined herein ashaving equal length sides, a rectangle is either a square or arectangle, and a 2 L rectangle 14 is a rectangle where the length istwice as long as the width. These two shapes fill the entire playingfield at all times. In an alternative example, which is not shown, othershapes may also be “legal,” such as a 1×4 rectangular shape in additionto or instead of the other previously mentioned shapes. Other shapes mayalso be utilized, as will be readily evident to those of skill in theart.

One concept of the game relates to the use of neighboring pieces. Inorder to win, one player's pieces must neighbor each other in chainsthat touch all four sides of the game board at one time. Examples ofpieces 16 that are considered to be neighboring are shown in FIGS. 1 and2. Pieces 18 that are not considered to be neighboring are shown inFIGS. 3 and 4.

The game involves a series of legal moves. Legal moves involve splittingor dividing legal pieces into smaller legal pieces, joining severalpieces together to define larger legal pieces, or swapping pieces withyour opponent's pieces. Legal pieces may be split, over multiple turns,into significantly smaller pieces. Smaller pieces may be joined togetherto create significantly larger pieces. There is no limit on the size ofthe pieces, other than pieces cannot be larger than the size of theplaying field. In the examples depicted in FIGS. 1-42, the pieces at alltimes must have a legal shape of either a square or a rectangle that istwice as long as wide. Very small pieces may be positioned next to verylarge pieces. Examples of legal 20 and non-legal 22 size pieces areshown in FIG. 5.

Typically, the example game is played by two players. In the depictedexamples, each game piece is either black or white. Alternately, thepieces could simply be two different colors, like blue and red or pinkand purple. The example game is not limited to a particular color, aslong as one player's game pieces are a first color and another player'sgame pieces are a different, second color. For simplicity in describingthe example game herein, black and white will be the colors used todescribe the first and second player's game pieces.

A piece can never be both white and black. However, pieces in theplaying field may regularly change color by swapping or switching thecolor of the pieces with the color of a piece of the other player.

In order to allow pieces to be divided or split, each player has asupply of smaller, legal-shaped pieces. For example, if a larger squarepiece is to be split in half into two smaller, rectangular pieces, theplayer would remove the larger, square piece from the playing field andreplace it with two smaller, rectangular pieces that together are thesame size as the removed piece. For another example, if an arbitrarynumber of smaller pieces together form the shape of a legal piece 20,the pieces may be combined into a single piece by joining them together.In this instance, the smaller pieces would be removed and replaced by asingle, larger piece.

While the above example involved splitting a piece into two legal shapedpieces, an alternative example could involve splitting a playing pieceinto a combination of legal shaped pieces. For example, a square piececould be split into four smaller squares, eight smaller 2 L rectangles,two squares and four 2 L rectangles, etc.

One starting position 24 for game play includes 18 white squares and 18black squares, all the same size, laid out in a 6-by-6 checkerboardpattern. This is shown in FIG. 6. Other example patterns for startingpieces may be a 3-by-8 checkerboard pattern, an 8-by-8 checkerboardpattern, or other similar patterns (not shown), the invention not beinglimited to a particular pattern.

In order to play the example game, players take turns moving, such as inchess. Either black or white may move first, but for ease of descriptionherein, black will typically be designated to move first. Players mayuse any method they like for determining who gets black and who getswhite. Each player may resign at any point, or both players may agree todeclare a draw.

With the game board layout of FIG. 6, game play begins with either asingle “split” or a single “join.” A player cannot pass so each turnresults in a distinct change in position on the playing field. A “split”is a move where a player takes their own piece and splits it into twosmaller legal pieces. For example, a player may divide a square piece inhalf into two 2 L rectangles or a 2 L rectangle may be divided in halfinto two squares. Splits may affect multiple pieces, as will beexplained in greater detail below. A “join” is a move where a playertakes several pieces and replaces them with a larger legal-shaped piece.The player may only split once or join once per turn and this must bethe first move. Splits and joins may be followed by swaps, which will bedescribed in greater detail below.

In the starting position 24 shown in FIG. 6, only a single piece mayinitially be split. With other examples, where the pieces do not startout in a typical checker board pattern, it may be possible to split morethan a single piece during the first move. As the game progresses,multiple pieces may be split in a single turn depending on the pieces'placement on the playing field. During a turn, a player's pieces may besplit or divided in two, so long as the two remaining pieces have alegal shape. Examples of splitting are depicted in FIGS. 7 a and 7 b. Aspreviously discussed, a square piece 26 may be split into two 2 Lrectangles 14 and a 2 L rectangle can be split into two squares 26.However, a 2 L rectangle 14 cannot be split lengthwise into two thinnerrectangles, because those rectangles would then be more than twice aslong as they would be wide.

Splitting multiple pieces is an extension of splitting a single piece.This involves extending the line of the split (“split-line”) 28 of asingle piece split. If the split-line 28 of a single piece is extended,a variety of scenarios may occur, some of which involve legal moves andother's of which would not be legal. These scenarios include:

(1) extended split line 28 will intersect piece belonging to theopposing player;

(2) extended split line 28 will hit edge of playing field;

(3) extended split line 28 will follow along border between two pieces;

(4) extended split line 28 will intersect one of the player's ownpieces, but not in such a way that creates two legal pieces; or

(5) extended split line 28 will bisect the player's own pieces in such away as to produce two legal pieces.

In the first, second, and fourth cases, the split-line 28 is not allowedto pass through the opposing player's pieces or the edge of the playingfield, or a friendly piece that would not be split properly, as thesplit would not be extended to those positions. In the third case, thesplit line 28 is allowed to follow the border between pieces until itcomes upon one of the other four possibilities listed. In the fifthcase, a multi-piece split may occur so that both the initial piece issplit and one or more other pieces are also split. The split occursalong a single split-line 28 and includes pieces immediately adjacentthe initial piece or following the border between pieces until itintersects other pieces of that player's. As many pieces as desired maybe split until an obstruction, as identified above, has occurred. Anobstruction defines the end of the split-line 28. The split-line 28 doesnot have to extend all the way to the obstruction. The player may stopthe splitting of pieces at any point along the split-line 28. Examplesof splitting multiple pieces are shown in FIGS. 8 a and 8 b.

The ability to split multiple pieces in a single move via a split-line28 gives players a powerful tool because it allows players to make alarge change to the playing field. The split-line 28 is like a “laser,”unable to burn its way through opposing pieces or the edge of the board,but able to continue in a straight line until it reaches an obstacle oruntil the player decides he or she has divided enough of their ownpieces in two. Once the “laser” is turned on, it splits every piece itencounters until the player decides to turn it off In other words, foras far as the player chooses to extend the split-line 28, all piecesmust be split. A player cannot leave some pieces along the split-line 28unsplit.

As an alternative to the rules described above, another example involvessplitting a player's own pieces even where the split line passes firstthrough an opponent's pieces. In addition, another example scenarioinvolves splitting an opponent's pieces, in addition to or instead ofsplitting a player's own pieces along a split line. Another alternativeexample involves allowing the split line to travel through pieces, butnot splitting all pieces along the split line. In this example, theplayer may pick and choose which pieces to split along a single splitline.

“Joins” occur when a player wishes to join several pieces together toform a single-legal shape. Essentially, the player takes a number ofpieces in the playing field and “dissolves” the borders between them toform a single legal piece. Examples of joining are depicted in FIGS. 9 aand 9 b. In practice, the player would remove the smaller pieces andreplace them with a single, larger legal-shaped piece on the playingfield. The piece has the same size and shape as the outer edge definedby the combined pieces being replaced.

In an alternative example, a join could include utilizing an opponent'spieces in order to form a legal shaped playing piece, such that anopponent's pieces are commandeered. For example, where a square space isoccupied by four equal sized squares, three of which are black and oneof which is white, in this example, the black player could join thethree black and one white piece to form a single black piece. Thedecision on whether a piece could be commandeered could be based uponpercentage of color (such as greater than 50% of one color allows aplayer to commandeer) or other rules. Other variations are alsopossible, as will be readily evident to those of skill in the art.

An alternative joining method could involve joining pieces into multiplelegal shaped pieces, rather than joining multiple pieces into a singlelegal shaped piece. For example, six legal shaped square pieces that arearranged in a rectangular shape could be joined into a larger squarethat occupies the space previously occupied by four of the squares and a2 L rectangle could replace the remaining two squares such that a squareand 2 L rectangle remains where previously six squares were present.

After a player has performed their “split” or “join,” they have theoption to perform a swap. Swapping is wholly voluntary. A swap mustinvolve one of the pieces that results from the split or join in theprevious phase of the player's turn. In other words, whenever a playermoves, first they'll operate on some cluster of pieces to do a split ora join, and then their turn may continue from that same cluster,swapping pieces in a chain out from that cluster, as explained below.Swaps must occur with contiguous pieces. The overall impression istherefore of a single action, in which some group of pieces are actedupon, and that action then continues in the form of a swap.

A single swap involves making one player's piece turn into theopponent's piece, and turning one of the opponent's pieces into theplayer's piece. What is meant by this is that the opponent's piece turnsinto the color of the player's pieces and the player's pieces turn intothe color of the opponent's piece. To do this, the two pieces are“swapped” by changing their colors. Once a player has identified thepiece of their own that they want to swap, the player can swap thatpiece with any opposing piece that borders it on a complete side.“Bordering on a complete side” means that one full side of the player'spiece must be entirely shared with one full side of the opponent'spiece. The shared sides must be not only substantially co-linear, butalso the same length, and occupy the same space. FIG. 10 shows anexample where pieces border on a complete side. When two corners of asingle piece touch two corners of another piece, this is referred to as“two-point” neighbors. Two-point neighbors are permitted to be swappedwith one another. FIG. 11 shows an example where pieces do not border ona complete side and are not two-point neighbors. Pieces that are nottwo-point neighbors may not be swapped with one another.

Swaps may occur in chains. In other words, once a player has performed asingle swap, the player can take the new piece that has just become hisor hers, and swap it with any other piece that meets the criteriadiscussed above for swapping. This can be performed as many times as theplayer would like. Once a player decides to finish swapping, their turnis over. Whenever players swap, each step that is taken along theswapping path is treated as a move of its own and it changes theconfiguration of color pieces on the board. If one of those steps winsthe game for either player, then the turn ends and the game is over.

FIG. 12 shows an example move where the first player splits a blackpiece and then swaps one of the split pieces with the second player'swhite piece. FIG. 13 shows another series of legal moves. In FIG. 13,the first player vertically splits a black piece and then proceeds toswap one of the black pieces first with a piece to the East, next with apiece to the South, next with a piece to the East, and finally with apiece to the North. So the end result is that the original black piece30 ends up as a white piece 32 and the final piece 34 is black.

Although swapping, as described above, requires that the playing pieceshare an entire common side with an adjoining piece, an alternativeexample involves allowing swapping when a playing piece does not sharean entire side. In this example, the sharing of a partial side isacceptable for swapping purposes. For example, if a playing piece ispositioned on the edge of the playing field and doesn't have room tobecome big enough to share a common side with an adjoining piece, therules may allow the player to swap even though the piece does not have acommon side with an adjacent piece. The same could hold true forcaptures, which are discussed in greater detail below.

In an alternative example, a player's turn can involve any combinationof splitting, joining, and swapping. For example, any of these moves canoccur first. A player could be limited to splitting only pieces thatwere previously swapped. Alternatively, a player could be limited tooperating on pieces that were not previously operated on during a priormove within that given turn. Many variations exist, as will be readilyevident to those of skill in the art.

A scenario that may arise as a result of a swap on behalf of eitherplayer is a “capture.” In captures, a piece is captured when some of theplayer's pieces completely surround the opponent's piece or pieces. Whenthis occurs, the surrounded opponent's piece(s) become owned by theplayer and assume the same color as the player's pieces. Capturingoccurs during a move when one or more of the opponent's pieces aresurrounded on all sides by the captor's pieces. Whether an opponent'spiece is surrounded sufficiently to allow for capture is defined by howthe captor's pieces border the opponent's pieces.

There are four ways that two playing pieces may border each other:

(1) on a complete side, as described above in connection with swapping;

(2) on some part of a side, more than just touching at a corner, but notnecessarily sharing a complete side together;

(3) on a complete side of the subject piece, while the adjacent piece islarger, but only shares a part of the side of the larger piece; and

(4) touching only at the tip of a corner.

If one player's pieces form a loop around the other player's pieces suchthat the player's pieces border each other according to (1), (2), and(3) above, then any opposing pieces within that loop are ‘captured’,i.e. they change color to be that of the captor. This occursautomatically and is not a matter of choice. If the loop contains somepieces that only border, but not at the tip of the corner, then the loopis insufficient for capture purposes. Multiple pieces may be captured ata single time, even though they might not be positioned around the outeredges of the group or bordering the outer edges. The loop defineseverything within itself that is captured. Capturing allows thebordering player to take over any pieces of the opponent that fall intothe captured area. It should be noted that captures cannot be performedagainst the edge of a playing field—all four sides of a piece must besurrounded in order for a piece to be captured.

Captures are assessed after each swap in a swap-chain. Thus, it ispossible to perform several captures in a given turn. It is alsopossible to swap into a given position solely in order to perform acapture, and then swap out again to a previous step along the swapchain, as part of the same turn. Captures are not part of moving, e.g.taking one's turn. They simply occur when an opponent's pieces aresurrounded. A player can also swap into a situation where his or her ownpieces may be captured. Captures are judged on a move-by-move basis.Examples of captures are shown in FIGS. 14-16. FIG. 14 depicts game playwhere a single piece 36 is captured. FIG. 15 depicts game play wheremultiple pieces 38 are captured. FIG. 16 depicts game play wheremultiple pieces 40 in an irregular pattern are captured.

An example turn of the first player is shown in progression in FIGS. 17a to 17 h, which shows swapping and capturing within the same turn. Thefirst configuration shown in FIG. 17 a depicts the anticipated chain ofmovement for the turn. First, a black 2 L rectangular piece is splitinto two squares. Then the white rectangular piece to the East isswapped with the black square as shown in FIG. 17 b. This results in acapture of the above white rectangle, as shown in FIG. 17 c. The whiterectangle becomes a black rectangle. The first player continues withanother swap to the East, as shown in FIG. 17 d. Again, the white squareabove is captured and becomes black, as shown in FIG. 17 e. The firstplayer continues by swapping to the East again, as shown in FIG. 17 f.As a result of this move, the two lower black pieces are now surroundedby the second player's white pieces and become captured and turned towhite, as shown in FIG. 17 g. The first player then swaps with therectangular piece to the South, as shown in FIG. 17 h. This results inthe black piece being captured by white, as shown in FIG. 17 i.

It should be noted that the first player could have ended the turnbefore any of the swaps that resulted in capture. In addition, the firstplayer could have swapped backwards into pieces that had already beenswapped through in order to avoid capture.

An alternative example involves assessing captures only at the end of aswap chain, such that captures are not assessed on a move by move basis.Captures are not optional in the above described example, but may beoptional if the rules are so defined. Where they are optional, theplayers may choose whether to capture on a move by move basis.

The captures described above involve capturing an opponent's piecesduring each move in a swap chain. However, an alternative exampleinvolves assessing whether a player's own pieces are captured during thesame swap chain, such that the black player's pieces can actually bechanged to white pieces during the black player's turn. In anotherexample, captures are only considered for pieces that are not currentlybeing swapped during a player's move. In another example, capturingwould only be permitted if the surrounding pieces share a complete sideinstead of a partial side.

A player wins the example game by getting all their pieces into awinning configuration or position. A winning configuration is one wherea player's pieces touch each of the four sides of the playing field andform a continuous chain of bordering playing pieces, such as an “X” orcross pattern. The winning configuration is defined in terms of theborder associations, as described above in connection with capturing. Inorder to form a winning configuration, one player must have piecesbordering each other according to at least one of items (1), (2), and(3) of the list described in capturing. In particular, the pieces musteither border each other along a complete side and/or must be touchingalong one of the sides, not including touching at a corner tip. Ifpieces in the chain only touch at a tip, it is not considered to be awinning configuration. One set of bordering pieces must link the top andbottom edges of the playing field together, and another set must linkthe left and right edges of the playing field. Symbolically, this meansthat the opposing forces have been shattered into fragments, a fittingway to decide the winner.

As with captures, the winning condition is assessed after each swap in achain. Thus, it is possible for one player to win on the other player'sturn, just as it is possible for either player to have their own piecescaptured on their own turn.

An alternative winning configuration could involve connecting the top tothe bottom with a continuous chain, or connecting the sides with acontinuous chain of pieces, instead of requiring both. Anotheralternative winning position could forego the continuous chain of piecesand simply involve assessing how much of the playing field is occupiedby a given player's pieces. For example, a winning configuration couldinvolve occupying 75% of the playing field, or 90% of the playing field,for example. Other examples are also possible. Another winningconfiguration could involve creating one or more pieces of a certainsize, such as, for example, a large square or a large 2 L rectangle.

Yet another alternative winning configuration involves surrounding youropponent's pieces in such a way that they are surrounded, as withcapturing. In this example, no capturing would be allowed during moves.The game may be won when a certain percentage or number of pieces aresurrounded, as with the rules for capture, discussed above. Anotherexample where no captures are permitted during normal play would involvea winning configuration where an opponent's pieces are surrounded insuch a way that the pieces that are surrounded do not share a completeside with any of the surrounding pieces. Another winning position wouldrequire that all the pieces in the continuous chain share a completeside.

When a player reaches a winning configuration, all outstanding capturesmay then be performed, if desired, so that the players can determine thefinal position of the playing pieces. This is not required.

A draw may be declared at any time if both players agree. There is,however, one situation where a game is automatically drawn. This occursif all the pieces that each player has split or joined on their mostrecent turn were also involved in splits or joins on that player'sprevious two turns, and if both sides have swapped into the same pieceon the most recent turn and the previous two turns. When this occurs,then game is automatically declared a draw.

Each example game set contains a variety of different-sized pieces. Whenyou decide to split a playing piece during the course of play, you takethat piece off the board and replace it with two smaller pieces. Thesame is true of joining—you remove the smaller pieces and replace themwith a larger piece. Playing pieces can be made from any type ofmaterial, including paper, cardboard, plastic, and the like. Forexample, playing pieces can be made with just paper and scissors, andplayers may choose to cut pieces during the course of play. If, duringthe course of play, a player wants to use a piece that is not availablein the set of pieces they have at their disposal, it is permissible totake a reasonable amount of time to make the desired piece out ofappropriate materials. Alternatively, a set of playing pieces may beprovided in advance in various sizes so there is little need to cutpieces during the course of play. Pieces may become arbitrarily small,so there may be times when the set of playing pieces is inadequate tohandle all moves. In that instance, players may choose to cut theplaying pieces to provide the proper size and shape. However, playerscan do whatever they want to effect the physical splitting of pieces.For more casual play, players may agree in advance to restrict the legalset of pieces to only those that are available to play with.

In an alternative example, captures could be prohibited or joins couldbe prohibited. Rules could exist where joins and captures are onlypermitted during certain times or for the first several minutes of play.Other variations are possible.

Referring again to the figures, FIG. 6 represents a starting position 24where the playing pieces are arranged in a 6×6 checkerboard-like grid.The playing pieces are flat, tile-like pieces in contrasting colors.They may be positioned on a flat surface, such as a game board surfaceor a table-top. All of the playing pieces are the same size in thestarting position and are square. There are 18 darker color or blackpieces 10 and 18 lighter color or white pieces 12. If an underlyingboard is being used in FIG. 1, it is completely obscured by the playingpieces. An underlying board could be used that defines a grid and thathas a larger footprint that the game pieces themselves (not shown). Aboard could also be provided where the game pieces are separated fromone another by small spacing (not shown).

FIG. 18 shows the playing pieces after a first move has been made by theblack player. In this case, the black player split a square playingpiece 40 into two rectangular pieces 42, 44. This created a common sidesurface 46 with white playing piece. The black player then, aftersplitting, swapped with the adjacent white piece such that white piecebecame black piece 48 and previously black piece became a white piece42.

FIG. 19 depicts a playing field 10 and playing pieces after many pieceshave been swapped, split and joined. The game pieces in FIG. 19 are atan intermediate position, with both black and white threatening to winin the next move. If one player is unable to prevent their opponent fromwinning on their next turn, that player is said to be in “crumble-mate.”Unlike in chess, it is not necessary to announce crumble-mate. The gamedoesn't end at mate, it ends when all four sides of the playing fieldare connected.

FIG. 20 depicts the playing field where the black player is about tomove and win the game and FIG. 21 represents the same playing field asFIG. 20 after the black player has made the winning move. As is shown bythe line 50 of black pieces in FIG. 20, the black player has connectingpieces that form a left arm 52 that touches the left side 54 and abottom arm 56 that touches the bottom side of the grid. There are also anumber of black pieces along line 50 that extend upwardly to the topside and to the right, but that do not have connecting surfaces thatjoin them to the top and right sides.

In order to move from the playing field in FIG. 20 to the playing fieldin FIG. 21, the black player first joins pieces 60, 62 and 64 into asingle square piece 66. Then the black player swaps in a swap chain theblack piece with white pieces 68 and 70 such that piece 70 ends up as ablack piece and piece 66 ends up as a white piece. The new black piece70 then provides a bridge between pieces 72 and 74 and provides themissing link for joining all four sides of the playing field in acontiguous chain, as shown by line. As is shown, line joins all foursides together in a contiguous chain 50 of black playing pieces, therebyfragmenting the white pieces into separate areas on the playing field,effectively “crumbling” the defenses of the white player.

FIG. 22 is similar to FIG. 18, but shows the playing field after adifferent first move has been made by the black player. In this example,the black player splits piece 76 into two 2 L rectangular pieces 78, 80and then swapped the black piece (previously 80) with the adjacent whitepiece 82 (shown as black after the swap).

FIG. 23 shows a similar playing field after many splits and swaps, butat an intermediate playing position where neither player is about towin. FIG. 24 shows the playing field of FIG. 23 at a later point intime, with the white player in a position where one move can win thegame and FIG. 25 shows the playing field after the white player hasmoved to win.

As is shown in FIG. 25, line 50 joins all four sides of the playingfield. Lines 84 and 86 in FIG. 24 show the disconnect prior to the moveto get to the winning position in FIG. 25. In order for the white playerto move to the winning position in FIG. 25, blank playing piece 88 mustbe turned into a white playing piece. In order to change piece 88 fromblack to white, the white player first performs a “join” and thenseveral swaps. First, the white player joins pieces 90 and 92 to make asingle piece 94. Because piece 94 shares a common border with adjacentpiece 96, pieces 94 and 96 can be swapped. Piece 96 is swapped withpiece 98 for the same reason. Finally, piece 98 shares a common borderwith piece 88, allowing pieces 98 and 88 to be swapped. This changespiece 88 from black to white and allows the user to create a constantline 50 of connected pieces joining all four sides of the playing field.

As with chess, the present game has a notation system for identifyingmoves. To make a move, you identify first the piece you wish to startwith, and then the additional pieces you plan to act upon. Examplenotations are shown below:

3,1V2-1W-NWN

3,1H

3,2HN-W

4,5J3,2

The notation system is a standard formula for identifying any piece andmove on the playing field. Each notation begins with the location of thepiece you intend to initially operate on with either a split or a join.The numbers reflect the location of the piece within the playing field,a V (for vertical) or an H (for horizontal) represents how a piece is tobe split, and a J (for join) represents that a piece is joined. The N,S, W, and E directional letters either represent which way the piece isto be moved directionally, or they are used to identify which part of asplit piece is to be moved. With the latter, a dash separates the pieceidentification nomenclature from the move nomenclature, where necessary.

An example notation for the location of the first piece might be 3,1. Inorder to identify the location of a piece, a player counts intersections100, and the numbers in the notation reflect the number of intersectionsto reach the bottom, left corner of the piece. An example showinglocation 0, represented by the large dot, is presented in FIG. 26. Anexample of location 3, represented by the large dot, is presented inFIG. 27. An example of location 0,3 102 is presented in FIG. 28. Anexample of location 2,2 104 is presented in FIG. 29.

After pieces have been split, the notation may require additionalnumbers in order to reach the bottom, left corner of the piece that isbeing operated on. For example, location 3,1,1 106, shown in FIG. 30,involves counting to the East by three intersections 100 from thebottom, left corner of the playing field, moving North by oneintersection 100, and moving East by one intersection 100. Location isalways identified by a series of East, North, East, North, etc. moves.For example location 3,3,1,1 108, shown in FIG. 31, the user firstcounts three intersections 100 to the East, three intersections 100North, one intersection 100 East, and one intersection 100 North inorder to reach the bottom, left corner of the target piece.

Joining is notated by using the letter J. First the bottom, left cornerof the starting piece is identified. This point establishes a new pointzero (0). Using the new zero (0) point, the player then countsintersections upwardly to the upper, right corner of the target joiningpieces to establish the boundary for the pieces to be joined. An examplehere is shown in progression in FIGS. 32 a and 32 b. The first gameboard in FIG. 32 a shows the pieces before being joined and the secondgame board in FIG. 32 b shows the pieces after being joined. Thenotation for this move is 4,3J5,4. First, the bottom left corner isidentified by moving 4 intersections East and 3 intersections North.Then this is set as the zero point and the player counts 5 intersections110 East and 4 intersections 112 North to establish the upper, rightboundary of the pieces to be joined together. The joined pieces 114 arethen shown in FIG. 32 b.

Once pieces have been joined, it is then possible to swap. In order toadd a swap to the notation, the direction of swap for the joined pieceis then added to the end of the notation. An example is shown in FIGS.33 a and 33 b. FIG. 33 a shows the pieces before being joined and FIG.33 b shows the pieces after they have been joined and swapped with apiece to the West. The full notation for this move is 2,1J1,2W. The twosmaller rectangles begin at location 2,1 114, which establishes a zeropoint. The end location for the join is one intersection 110 East and 2intersections 112 North of the zero point, or 1,2 from the original 2,1point. The two smaller rectangles are joined together to make a 2 Lwhite rectangle 116. This 2 L white rectangle is then swapped with theblack square to the West so that the black square to the West becomeswhite 120 and the 2 L rectangle to the East 118 becomes black 122.

FIGS. 34 a and 34 b depict an example of splitting one piece along avertical split-line. FIG. 34 a shows the playing field before the pieceis split and FIG. 34 b shows the playing field after a piece has beensplit and swapped. The notation for this move is 3,2VE. The pieces thatis to be split is located at 3,2, noted by the large dot. The “V”identifies that the piece is to be split vertically. The “E” identifiesthat one of the remaining pieces is swapped to the East. Since only thesplit piece that is to the East can be swapped with a piece to the West,it is not necessary to notate which piece is being swapped, since thechoice is inherent given the swap to the East. There are other timeswhere it is necessary to identify which of the remaining pieces is to beswapped and later examples describe this scenario.

FIGS. 35 a and 35 b depict an example of splitting one piece along ahorizontal split-line 28. FIG. 35 a shows the playing field before thepiece is split and FIG. 35 b shows the playing field after the piece hasbeen split and swapped. The notation for this move is 2,2HS. The piecesthat are to be split are located at 2,2, as noted by the large dot. The“H” identifies that the piece is to be split horizontally along splitline 28. The “S” identifies that the lower remaining piece is swapped tothe South. As with the prior example, since only the lower piece can beswapped to the South, it is not necessary to notate which of the twopieces are being swapped. The choice is inherent given the swap to theSouth.

FIGS. 36 a and 36 b depict an example of splitting a single piecehorizontally and swapping it in the direction of the split-line. FIG. 36a shows the playing field before the piece is split and FIG. 36 b showsthe playing field after the piece has been split and swapped. Thenotation for this move is 3,2HN-W. This notation includes a dash (“-”),which is different from prior notations. The dash in this case is usedto separate the identification of the piece being swapped from thedirection of swap. The piece that is being split is located at 3,2,noted by the large dot. The “H” identifies that the piece is being splithorizontally. The intended swap is to the West. However, both the upperand lower remaining pieces have the opportunity to be swapped to theWest.

Therefore, it is necessary to identify which of the two pieces is to beswapped. This is accomplished by notating the direction of the piecethat is being swapped. In this case, the northern piece 124 is the onethat is being swapped West, so the notation includes an “N” to identifywhich of the two pieces are being swapped and a dash separates thenotation for the identification of the piece from the swap movement,which is “W” for west. If the lower piece 126 of the two had been chosenfor swapping (which in this case was not possible since you may not swapa black piece with another black piece), the notation would have been an“S” before the dash. Thus, the dash is used to separate the move itselffrom the notation that identifies which piece is being moved. But whenit is not necessary to identify the pieces that is being moved, the dashis not necessary and the direction identifiers are used to identify thedirection for swap, as with prior examples.

FIGS. 37 a and 37 b depict an example where multiple pieces are splitalong a split-line 28. FIG. 37 a shows the playing field before thesplit and FIG. 37 b shows the playing field after the split. In thisexample, all the pieces being split are positioned adjacent one another.Therefore, three larger squared 128 turn into six 2 L rectangles 130.The notation for this move is 1,1H3. The starting point for the split isposition 1,1, noted by the large dot in FIG. 37 a). The split occurshorizontally, as denoted by the “H,” and the split occurs for threepieces 128 to the right or East. With horizontal splits, the number ofpieces to be split always occurs to the right or East of the initiallocation.

FIGS. 38 a and 38 b depict an example where multiple pieces are splitalong a split-line 28 in order to split two different pieces 132, 134,but where the split line also travels along an existing border line 136where pieces are not split. FIG. 38 a shows the playing field before thesplit and FIG. 38 b shows the playing field after the pieces have beensplit. The notation for this move is 3,1V2. The starting location is at3,1, noted by the large dot in FIG. 38 a). The “V” identifies that thepieces are split vertically and the “2” denotes that two pieces aresplit. Because this is a vertical split, the number of pieces to besplit always occurs to the North of the initial location. Here, sincethe split line runs along an existing border line 136, the split piecesare spaced apart from one another.

FIG. 39 depicts an example of splitting multiple pieces and swapping oneof the split pieces. FIG. 38 a represents the playing field before thepieces have been split and FIG. 39 represents the playing field afterthe pieces have been split and swapped. Because multiple pieces weregenerated by the split, it is necessary to identify which of the piecesare to be swapped. Dashes are used to separate the notations in order toidentify which pieces are split and which pieces are swapped. Thenotation for this move is 3,1V2-1E-ENE. The starting position is 3,1.The “V” identifies that a split is to occur vertically, and the “2”identifies that two pieces are split. This leaves two upper split pieces138 and two lower split pieces 140. A “1” is used to identify the lowersplit pieces 14 and a “2” would be used to identify the upper splitpieces 138. In order to separate this notation from the notation for thesplit, a dash is used. Because there are two lower pieces 140,represented by the “1,” the user uses an “E” to identify that theEastern piece 142 of the lower two is being swapped. This identificationis separated from the swap moves by a dash. Then the swap moves areidentified in the previously described fashion. In this case, the 1Epiece is first swapped East, then North, then East.

FIG. 40 depicts another example of splitting multiple pieces andswapping one of the split pieces. FIG. 38 a represents the playing fieldbefore the pieces have been split and FIG. 40 represents the playingfield after the pieces have been split and swapped. Because multiplepieces were generated by the split, it is necessary to identify which ofthe pieces are to be swapped. Again, dashes are used to separate thenotations in order to identify which pieces are split and which piecesare swapped. The notation for this move is 3,1V2-1W-NWN. The startingposition is at 3,1. The “V” identifies that a split is to occurvertically, and the “2” identifies that two pieces are split. Thisleaves two upper split pieces 138 and two lower split pieces 140. Inorder to properly identify which piece is being swapped, a dash ispositioned between the split notation and the notation that identifiesthe piece to be swapped. In this case, the lower, West piece is beingswapped, as represented by a “1W.” Then a dash separates theidentification of the piece 144 being swapped and the directions forswap. The selected piece is then swapped first North, then West, andthen North.

FIG. 41 depicts another example of splitting multiple pieces andswapping one of the split pieces. FIG. 38 a represents the playing fieldbefore the pieces have been split and FIG. 41 represents the playingfield after the pieces have been split and swapped. Because multiplepieces are generated by the split, it is again necessary to identifywhich piece is to be swapped. As with before, dashes are used toseparate the split notation from the piece identifying notation from themovement notation. The notation for this move is 3,1V2-2E-ESE. Thestarting position is 3,1. The “V” identifies that a split is to occurvertically, and the “2” identifies that two pieces are split. Thisleaves two upper split pieces 138 and two lower split pieces 140. Inorder to properly identify which piece is being swapped, a dash ispositioned between the split notation and the notation that identifiesthe piece to be swapped. In this case, the upper (denoted by a 2), Eastpiece 146 is selected for swapping, as represented by a “2E.” Then adash separates the identification of the piece being swapped and thedirections for swap. The selected piece is then swapped first East, thenSouth, and then East.

FIG. 42 depicts yet another example of splitting multiple pieces andswapping one of the split pieces. FIG. 38 a represents the playing fieldbefore the pieces have been split and FIG. 42 represents the playingfield after the pieces have been split and swapped. Because multiplepieces are generated by the split, it is necessary to identify whichpiece is to be swapped. Since there were two pieces that were split,this leaves a lower block of split pieces 140, represented by a 1, andan upper block of split pieces 138, represented by a 2. As with before,dashes are used to separate the split notation from the pieceidentifying notation from the movement notation. The notation for thismove is 3,1V2-2W-WSSE. The starting position is 3,1. The “V” identifiesthat a split is to occur vertically and the “2” identifies that twopieces are split. This leaves two upper split pieces 138 (represented bynumber 2) and two lower split pieces 140 (represented by number 1). Inthis case, the upper, West 148 split piece is selected for swapping.Then a dash separates the identification of the piece being swapping andthe directions for swap. The selected piece, in this example, is swappedWest, South, South, and East.

While the above examples are discussed in the context of using squaresand 2 L rectangles, other embodiments of the invention may incorporateother shapes. The substitution of different shapes involves onlyminimally adjusting the rules of the game in order to allow differentpieces. The effect of these substitutions on game play, however, can beprofound. Some other shapes that are contemplated include Goldenrectangles 150, Silver rectangles 160, and A4 rectangles 170. Goldenrectangles 150 are shown in FIG. 43, Silver rectangles 160 are shown inFIG. 44, and A4 rectangles 170 are shown in FIG. 45. The use of silver,golden, or A4 rectangles increases the number of available moves andsubtlety changes the deeper structure of play.

Golden rectangles 150 are rectangles whose side lengths are in thegolden ratio, 1:φ (one-to-phi), that is

1:(1+√/5)/2 or approximately 1:1.618.

A special feature of the golden rectangle is that when a square section152 is removed, the remainder is another golden rectangle 150 with thesame proportions as the first. This square removal can be repeatedindefinitely. Thus, an example game is contemplated utilizing aplurality of squares that may be broken into legal pieces that includeeither a golden rectangle 150 or a square 152. When pieces are split,they may be split into a square 152 and a smaller golden rectangle 150.

Silver rectangles 160 are rectangles that have side lengths thatrepresent the silver ratio of

1:(1+√2)≈2.4142

A special feature of the silver rectangle 160 is that removing thelargest possible square from a silver rectangle 160 yields anothersilver rectangle. An example game is contemplated utilizing a pluralityof squares and silver rectangles.

A4 rectangles 170 have a unique property wherein they possess a ratio of1:√2. The A4 rectangle 170 can be split widthwise to produce tworectangles 170 whose sides have the same ratio as the original piece, asshown in FIG. 45. Thus, instead of having a square and a 2 L rectangle(having a ratio of 1:2), the use of A4 rectangles 170 would producepieces with a ratio of

(x/2):(x*√2).

These pieces are referred to has half A4 pieces 172. There is astrategic significance to using the A4 170 and half A4 172 piecesinstead of the square and the 1:2 rectangular pieces. In the gamedescribed above in connection with FIGS. 1-42, the rectangle (1:2 ratio)only has one way that it may be split, which is widthwise, producing twosquares. Squares have two ways they can split, either lengthwise orwidthwise, which produces two rectangles in either case. With A4 170 andhalf A4 172 playing pieces, the half A4 pieces 172 also have only oneway to be split, which is widthwise, producing two A4 pieces 170. Butthe A4 pieces 170 can be split lengthwise to produce two half A4 pieces172, or widthwise to produce two more A4 rectangles 170. Instead of thecase of the square being able to produce only rectangles that in turnhave only a single option of how they can be split, the A4 pieces 170can split into two more A4 pieces 170 that in turn have two options ofhow they can be split. In the parlance of game theory, this means thatthe game described in FIGS. 1-42 has a “less bushy game tree” than thegame that may be played with A4 170 and half A4 pieces 172.

Similarly, other pieces may be constructed, either quadrilateral, or anypolygon or curved shape that may be split and joined in a way to producea game tree such as that described above.

The above examples were defined in terms of a two person game. However,one of skill in the art will recognize that this game may also be playedby more than two players. Where there are more than two players, anadditional color of pieces shall be added, such as a third color. Thegame pieces will preferably be arranged in an organized pattern toaccommodate the additional person or persons. Other variations will bereadily apparent to one of skill in the art based upon the teachingsherein.

The term “substantially,” if used herein, is a term of estimation.

While various features of the claimed embodiments are presented above,it should be understood that the features may be used singly or in anycombination thereof. Therefore, the claimed embodiments are not to belimited to only the specific embodiments depicted herein.

Further, it should be understood that variations and modifications mayoccur to those skilled in the art to which the claimed embodimentspertains. The embodiments described herein are exemplary. The disclosuremay enable those skilled in the art to make and use embodiments havingalternative elements that likewise correspond to the elements recited inthe claims. The intended scope may thus include other embodiments thatdo not differ or that insubstantially differ from the literal languageof the claims. The scope of the example embodiments is accordinglydefined as set forth in the appended claims.

1. A game of strategy comprising: a plurality of game pieces that aredividable into smaller game pieces, said game pieces initiallycomprising some in a first color and some in a second color, andarranged in a pattern on a playing surface to define a playing field,with each of the pieces having a legal shape such that the pieces mayonly be divided into legal shapes.
 2. The game of claim 1, wherein halfof the pieces are a first color and half of the pieces are a secondcolor.
 3. The game of strategy of claim 1, wherein a legal shape for thegame pieces is either square or a 2 L rectangle.
 4. The game of strategyof claim 1, wherein a legal shape for the game pieces is either squareand golden rectangle or square and silver rectangle.
 5. The game ofstrategy of claim 1, wherein the game pieces are dividable, but onlyinto smaller, legal-shaped game pieces.
 6. The game of strategy of claim1, wherein the game pieces may be joined to form a single legal-shapedgame piece from a plurality of game pieces.
 7. The game of strategy ofclaim 1, wherein the game pieces of the first color may be swapped withgame pieces of the second color and vice versa.
 8. The game of strategyof claim 1, wherein in order to swap pieces, said pieces must share acommon width or length.
 9. The game of strategy of claim 1, wherein inorder to divide the game pieces, a split line is defined and anylike-colored game pieces along said split line are dividable.
 10. Thegame of strategy of claim 1, wherein the game pieces of the first colormay be captured by the game pieces of the second color and vice versa.11. The game of strategy of claim 1, wherein in a starting position,half of the pieces are a first color and half of the pieces are a secondcolor, the game pieces are dividable into smaller game pieces, multiplegame pieces may be joined to form a single game piece from a pluralityof game pieces, the game pieces of the first color may be swapped withgame pieces of the second color and vice versa, and the game pieces ofthe first color may be captured by the game pieces of the second colorand vice versa.
 12. A game of strategy comprising: a plurality ofplaying pieces, each playing piece being dividable into two playingpieces and being arranged in a pattern on a playing surface, wherein theplaying pieces may be one or more of divided, joined, swapped, andcaptured during play, wherein the playing pieces comprise a first set ofpieces having a first color and a second set of pieces having a secondcolor.
 13. The game of claim 12, wherein, during play, one or moreplaying pieces may be captured such that said one or more playing pieceschange from either the first color to the second color or from thesecond color to the first color.
 14. A process for playing a game ofstrategy having a plurality of playing pieces that are dividable,joinable, swappable, and capturable, said playing pieces being arrangedin a pattern on a playing surface, said playing pieces including a firstset of pieces having a first color and a second set of pieces having asecond color, said process comprising: a first move that includessplitting one playing piece of the first color into two smaller playingpieces of the same color and optionally swapping one of the splitplaying pieces of the first color with one of the playing pieces of thesecond color; a second move that includes either splitting one or moreplaying pieces of the second color into two or more smaller pieces ofthe second color or joining two or more playing pieces of the secondcolor into a single larger playing piece of the second color andoptionally swapping one of the split or joined playing pieces of thesecond color with one of the playing pieces of the first color; afurther move of one or more playing pieces of the first color thatincludes one or more of splitting, joining, or swapping; and a furthermove of one or more playing pieces of the second color that includes oneor more of splitting, joining or swapping.
 15. The process of claim 14,wherein initially half of the playing pieces are the first color andhalf of the playing pieces are the second color.
 16. The process ofclaim 14, further comprising assessing whether one or more playingpieces have been captured during each move, with capturing involvingsurrounding one or more playing pieces of the other color.
 17. A winningposition for a game of strategy having a plurality of game piecesarranged on a playing surface, the pieces being arranged in a patterndefining a playing field that has a West side; an East side, a Northside, and a South side, with the game pieces being split into a firstset having a first color and a second set having a second color, saidwinning position comprising: a contiguous chain of game pieces of asingle color that extends between at least two of the West Side to theEast side to the North Side to the South side.
 18. The winning positionof claim 17, wherein the winning position requires a contiguous chain ofgame pieces that extends between all four sides from the West side tothe East side to the North side to the South Side of the playing field.19. The winning position of claim 17, wherein the game pieces abut eachother along at least part of the length or width of one of their sidesto form the chain.